Basic Concepts of A Machine
Basic Concepts of A Machine (1)
 Stator: stationary portion of the machine
 Rotor: rotating portion of the machine
 Shaft: the stiff rod that the rotor is mounted on
 Air gap (Gap): between stator and rotor
Basic Concepts of A Machine (2)
 Load current: the current that varies with load
 Magnetizing current: provide magnetic field and independent of load
 Armature: the winding that carries only load current
 Field: the winding that carries only magnetizing current
 dc machine: the input/output current is dc
 ac machine: the input/output current is ac;
two categories: synchronous machine
induction machine (no field winding,
similar to transformer)
Basic Concepts of A Machine (3)
Basic Concepts of A Machine (4)
round rotor
salient pole rotor
Electrical vs Mechanical Frequency
N
S
S
N
N
S
S
N
At steady state
mechanical speed n m
fm
P
fe  fm
2
revolution/minute (rpm)
nm
1
 nm

60
60
rev/second
Slots and Coils (1)
Double Layer Lap Winding
bottom
top
tooth
slot
top
bottom
Slots and Coils (2)
coil end
coil side
coil leads
coil side
coil end
Nc turns, 2Nc conductors
Slots and Coils (3)
On armature
 Each slot has 2 positions: top and bottom (double layer winding)
 Each coil needs to occupy 2 positions: top position of one slot
and bottom position of another slot
Number of armature coils = Number of armature slots (S)
S
Number of coils per phase : S ph 
m phase machine:
m
S  Nc
Number of turns per phase: N ph  S ph Nc 
m
S  Nc  2
Number of conductors per phase: C ph  2 N ph =
m
Note: The above three equations are independent of the
number of poles (P). For balanced m-phase design, Sph
should be an integer.
Slots and Coils (4)
3 phase, 24 slots
8 coils, 8Nc turns, 16Nc conductors per phase
13 12 11 10 9
N ph  8 N c
8
7
6
turns 5
4
3
2
1
2 pole, Phase A, full-pitch
7
6
N ph
 4 N c turns 5
P/2
4
2 3
1
4 pole, Phase A, full-pitch
Slot Pitch
Slot pitch in electrical angle is defined by
 
P
m
2
where m is the mechanical angle between two adjacent slots:
m 
2
S
 
P
S
The slot pitch is also defined as the arc length between two
slots on stator inner circle (with diameter D):
s 
D
S
13 1211 10 9
m
D
3 phase, 24 slots, 2 pole
Phase A, full-pitch
1
2
8
7
6
5
4
3
Pole Pitch
Pole Pitch: angular distance between two adjacent poles on a machine.
360 o 2
P 

P
P
(in mechanical degree)
Regardless of the number of poles on the machine, a pole pitch is
always 180 o or  in electrical degrees.
The pole pitch is also defined as the arc length between two adjacent
poles on stator inner circle (with diameter D) :
P 
D
P
(in meter or inch)
Number of Slots per Pole:
SP 
S
P
Note: SP may not be an integer.
36s8p
SP 
36
 4.5
8
Coil Pitch
Full-Pitch Coil: If the armature coil stretches across the same angle as
the pole pitch, it is called a full-pitch coil. The coil spans across SP
slots, if SP is an integer.
Fractional-Pitch Coil: If the armature coil stretches across an angle
smaller than a pole pitch, it is called a fractional-pitch coil (or shortpitched coil, chorded coil) . The coil spans less than SP slots.
Let Sc be the number of slots that the coil spans.
Let m be the mechanical angle that the coil spans or  m  Sc m .
Coil pitch in electrical angle is defined by

  m Sc


 P SP

P
m
2
Fractional Pitch Coil (1)
24 slots, 2 pole, 3 phase
m
13 12 11 10 9
m
m
1
2
2

2
2 


24 12
P 
 m 
8
7
6
5
4
3
Phase A, full-pitch
   m    180 o

12
12 11 10
9
m
1
2
8
7
6
5
4
3
Phase A, (11/12)-pitch
  m 
11
  165o
12
Fractional Pitch Coil (2)
24 slots, 4 pole, 3 phase
2 

4
2
2 


24 12
P 
m
m
7
6
5
1
2 3
m
4
1 2
4
2
  m 
Phase A, full-pitch
m 

2
 90 o
    180 o
6
5
3
4

6
Phase A, (5/6)-pitch
5  5
m 

 75o
6 2 12
5
6
    150 o
Group (1)
4 pole, 3 phase, 24 slot machine
Phase A, (5/6)-pitch
This group consists of 2 coils.
Number of coils per group:
Number of Stator Slots ( S )
Number of phases (m)  Number of poles ( P )
S
for 3 phase machine
q
3P
q
Number of coils = Number of slots for double layer winding
Number of groups = Number of poles (P) for double layer winding
Group (2)
q can take fractional number
q
18
 1. 5
3 4
4 pole, 3 phase, 18 slot
q
9
 1. 5
3 2
2 pole, 3 phase, 9 slot
Torque
UCF
T  RF
T
0
F
R
How to understand torque:
Put the thumb in the direction of torque.
The other four fingers point to the direction of rotation.
wrench on a nut
Torque from a Current Loop
UCF
d F1  Idx a x  B  Idx ( B y a z  B z a y )
R1  
1
dy a y
2
1
dy a y  Idx ( B y a z  B z a y )
2
d T1  R 1  d F1  
1
dxdyIB y a x
2
1
d T3  R 3  d F3  dy a y  (  Idx )( B y a z  B z a y )
2
1
  dxdyIB y a x  d T1
2
d T1  d T3   dxdyIB y a x

Bloop
Likewise d T2  d T4   dxdyIB x a y
 Idxdy ( a z  B )  Id S  B
Define d m  Id S  d T  d m  B
Note:
dm is in the same direction of Bloop and
both are proportional to I

dm = k Bloop
d T  kB loop  B
UCF
Torque Property of a Machine (1)
T  kB R  B S
T  kB R BS sin 
Since B net  B R  B S
T  k B R  ( B net  B R )
 k B R  B net
T  kB R Bnet sin 
UCF
Torque Property of a Machine (2)
BR
Bnet
6 pole synchronous machine
Torque Property of a Machine (3)
UCF
T  kB R  B S
generator
motor

